Charging Profile Modeling of Electric Trucks at Logistics Centers

Abstract

The future charging requirements of electric trucks will lead to new demands on the power grid. In order not to slow the expansion of the charging infrastructure for electric trucks, the power grid must be strengthened for this purpose. However, due to the limited penetration of electric trucks in fleets to date, grid planners lack information on their time- and location-dependent charging demand. The question arises as to how the charging demand of electric trucks can be realistically taken into account in power grid simulations. This paper therefore presents a methodology that makes it possible to quantify the charging demand of electric trucks at typical charging locations and derives initial parameters for power system planning with electric trucks. For location-based charging demand modeling, the arrival and departure behavior of trucks at representative logistics centers is combined with mobility data and vehicle parameters. This allows the determination of time series-based charging demand. A charging demand analysis at five different logistics center types shows that that energy demand, peak load, and temporal behavior vary greatly depending on the center type. It is therefore advisable to take these different charging location types into account when designing the electricity grids.

1. Introduction

The European Climate Law sets out clear targets for achieving climate neutrality in the European Union (EU) by 2050, requiring countries to reduce their greenhouse gas emissions by at least 55% compared to 1990 levels by 2030 [1]. A fifth of all greenhouse gas emissions in the EU are caused by road transport, with CO₂ accounting for 99% of this [2]. However, these emissions have not yet fallen across the EU, but have increased by over 20% compared to 1990 [2]. This sector therefore needs to be significantly more involved in reducing emissions than before, especially since there are only a few years left until 2030. One of the main measures here is the replacement of internal combustion vehicles by zero-emission vehicles, mainly battery electric cars, which have experienced a strong ramp-up in Germany in recent years. With a stock of more than 1.3 million battery electric passenger cars in 2023, this corresponds to almost 3% of the total passenger car fleet in Germany [3]. However, it will not be enough to focus solely on the passenger car segment in order to achieve the climate targets. In the EU, cars and motorcycles account for around 60% of CO₂ emissions from road transport, but two other relevant contributors are buses and heavy goods vehicles, with 28%, and light commercial vehicles, with 12% [2].

In order to achieve the climate targets, alternative drive concepts must also be used in the field of road freight transport. Emission-free drive technologies can be battery, hydrogen fuel cell, and overhead line trucks. In [4], the sales forecasts for heavy trucks determined from clean-room talks with commercial vehicle manufacturers are presented. According to the truck manufacturers, around 75% of new registrations in Germany and 60% of new registrations in Europe should be emission-free by 2030. With a share of more than 75% in both Germany and Europe, battery electric powertrains dominate among emission-free heavy trucks [4]. Several studies have already dealt with economic analyses and comparisons of different drive technologies in the truck segment [5]. In [6], it was determined that battery electric semi-trailers in Europe will already reach total cost of ownership (TCO) parity with diesel trucks this decade, even without political subsidies. In [7], the life cycle costs of different truck drive technologies were compared to battery electric trucks. Compared with hydrogen fuel cell trucks, battery electric trucks performed significantly better in both [8]. Although the share of battery electric trucks in the total stock of Germany is currently low, at 2% [9], both manufacturers’ forecasts and economic studies indicate that a significant increase in the fleet share of these vehicles can be expected in the coming years.

The ramp-up of battery electric trucks creates a new charging demand for which the electric energy system has so far been little prepared [10]. In order to integrate the charging of electric trucks into power system planning, regionalized information on their charging requirements is needed. This can be time series-based or standard load profiles of the charging demand, but also characteristic values of peak loads. Due to the low market penetration of electric trucks in fleets, empirical values and historical data of their charging demand are lacking. However, in order to provide time-series and peak load values for grid planning, modeling approaches are required that quantify the truck charging demand synthetically. Existing studies on the charging demand of battery electric trucks often focus on single aspects like individual truck weight classes, exemplary charging locations, or fixed charging regions. The methods and results of these individual use cases often cannot be applied directly to power system planning. There is a lack of transferable electric truck charging demand models on the one hand and the derivation of characteristic charging profiles and peak loads for grid planning on the other. The aim of this paper was therefore to develop a transferable methodology for modeling the charging demand of battery electric trucks at logistics centers and to analyze their charging demands in order to simplify the consideration of electric truck charging in grid planning. In the following chapters, the state of the research will be discussed first, before the methodology developed is presented and the resulting charging demand is analyzed.

2. Literature Overview of Charging Demand Modeling and Grid Integration of Battery Electric Trucks

The following sections summarize the methods and results of the literature. The identified research gaps are then discussed, as well as the objective of this paper and its demarcation from the literature.

The objectives of the different publications in the area of grid integration of battery electric trucks vary widely. Ref. [11] aimed to estimate the charging behavior and charging needs of battery electric trucks for the U.S. in terms of locating their charging infrastructure and quantifying their required charging power. The impact of different battery sizes on charging behavior in local, regional, and long-distance transportation is investigated [11]. In [12], a charging network for electrifying long-distance trucks in Germany is modeled. Ref. [13] deals with charging infrastructure planning for intercity transportation in China. A method to calculate optimal charging schedules for heavy-duty electric trucks at rest areas and rest stops in the U.S. was developed in [14]. An approach to optimize charging infrastructure and charging schedules for a logistics network is proposed in [15]. Ref. [16] compares the use of battery electric trucks with overhead line trucks in Canada, whereas ref. [17] optimizes battery swapping for electric trucks. Ref. [18] quantifies the charging demand of electric trucks at depots and the charging impact on distribution substations. Ref. [19] investigates the use of a charging management system for medium- and heavy-duty electric trucks at depots to reduce peak loads and energy costs. Ref. [20] also deals with the smart charging of trucks at a factory. Ref. [21] investigates the influence of fast charging infrastructure for trucks on the grid, focusing on the potentials of voltage regulation. The challenges of fast and megawatt charging infrastructure for battery electric trucks in terms of charging configurations, grid connections, and investments are quantified in [22]. Ref. [23] analyses the reliability of power supply systems for electric roads to charge electric trucks. Ref. [24] focuses on the optimal operation of electric vehicles in a logistics network tailored to generation and load fluctuations in a microgrid. Electric vehicles can not only charge but also discharge and thus contribute to overall optimal operation of the system [24]. In contrast, Ref. [25] aimed to determine the probabilistic mobility and charging profiles of commercial electric vehicles for low- and medium-voltage grid planning. Ref. [26] compares the flexibility potentials of different fleets determined from real charging data. Ref. [27] also looks at the flexibility potential of electric trucks and buses.

Within the studies, different methods have been used to model the trucks’ charging demand. For example, ref. [11] uses telemetry data from truck trailers combined with fixed battery sizes to determine and locate the charging demand of the vehicles. While ref. [14] calculates all routes between one combination of origin and destination, ref. [18] uses real-world data from the driving cycles of three real heavy-duty fleets and generates the charging demand of individually assembled fleets with a fixed consumption. Ref. [21] uses a model based on queueing and telemetry data to estimate the charging demand at individual fast-charging sites. Ref. [22] combines truck mobility data with data on arrival and departure of logistics business areas and regulatory frameworks. The charging demand modeling in [28] is again based on a large-scale simulation of the transport volume in a model region. In [24], on the other hand, a logistics benchmark model with a fixed number of logistics hubs is used, and the journeys between the hubs are optimized. Ref. [25] uses trip data from Germany and generates probability distributions to model new driving profiles and derive load profiles from these. In [26], real charging data of battery electric vans at a depot were used. Regardless of which type of electric vehicle is considered, charging demand modeling approaches in the literature can be divided into three categories:

• Approaches based on real measurement data of the charging demand;
• Approaches based on the simulation of mobility behavior of the vehicles;
• Approaches based on the simulation of the behavior of vehicles at fixed locations.

In some cases, there are also mixed forms of the three categories. The specific design of the modeling in the three categories differs depending on the publication. In the field of battery electric trucks, due to the very low registrations currently, real measurement data of the charging demand, as in [26], are available only to a very small extent and for a few vehicles and vehicle classes. Approach 1 is therefore currently less suitable for transferring to electric trucks. With increasing electric truck registrations, this approach may become more interesting in a few years, especially in order to further validate the synthetic charging demand modeling from approaches 2 and 3 and to identify behavioral changes due to the electrification of trucks.

Charging demand modeling approaches according to categories 2 and 3 can be classified as synthetic charging profile modeling. This means that the charging demand is determined based on current data on the behavior of conventional vehicles combined with information on the consumption and range of electric vehicle models. Approaches falling into category 2 determine the charging demand of battery electric trucks based on the simulation of the mobility behavior of conventional trucks. By linking the mobility behavior with data on consumption and range of battery electric trucks, the necessary charging processes can be integrated into the mobility behavior. This allows a time-dependent determination of the charging demand of the trucks and a derivation of charging profiles from this. The approaches to this often differ in the availability of GPS data. For example, [11] used telemetry data from U.S. trucks, which offered the advantage that the charging demand can also be located spatially precisely. Ref. [13] also used GPS data to identify truck stops in China. In contrast, many European studies, such as [25,29], used anonymized mobility data, which allow conclusions on specific routes and timestamps, but regionalize the positions of the trucks only according to location types and not according to their coordinates. Because of their focus on the mobility behavior of each individual vehicle, in this paper, these approaches are called vehicle-based.

For category 3, the determination of the charging demand is not focused on the individual vehicles, but on specific charging locations, such as depots or hubs on highways. In the context of this paper, these approaches are called location-based. Location-based charging profile modeling approaches quantify the charging demand based on the arrival behavior of conventional vehicles at these locations combined with mobility behavior and vehicle parameters of electric vehicle models. Approaches of this kind transferred to electric trucks can be found in [20,30,31]. Despite different implementations of the modeling, in the literature, location-based approaches are usually applied only to individual charging sites: in [22], these sites are two logistics business parks, and in [30], one real logistics center. This is also due to the high diversity of the logistics industry, which makes the development of transferable approaches particularly complex.

The types of vehicles and charging locations studied in the literature are diverse. Ref. [11] focuses on heavy-duty semi-trailers and looks at the U.S. regionally. In doing so, charging the trucks is integrated into truck driving cycles. Ref. [18] focuses on local heavy-duty trucks at different depots. Ref. [19] also deals with the charging of medium- and heavy-duty trucks at depots. Ref. [21] in turn deals with unspecified truck size classes at single fast-charging sites with one, three, or six charging points. In [22], long-distance trucks and their charging at three prototype charging sites (two logistics-cum-business parks and a charging hub near the highway) are considered. On the other hand, an abstracted model depot as well as 30 surrounding customers and three charging stations are dealt with in [24], but with the Chery E8, the data of the modeled electric vehicles are based on a passenger car model. Ref. [25], on the other hand, focuses on commercial road transport, but only on passenger cars and light commercial vehicles. Ref. [26] deals with a logistics depot in addition to passenger car charging stations, but only examines the use of light delivery vehicles such as vans. Ref. [28] concentrates on light-, medium-, and heavy-duty vehicles in Texas.

In addition to the methods for modeling charging demand as well as vehicle types and charging locations, the publications also differ with regard to the consideration of grid integration. The results on the regionalized charging demand of trucks in the U.S. in [11] are not analyzed with regard to their impact on the power grid. Using distance to the nearest substation, secondary conditions for the power grid are taken into account in the positioning of the charging network for trucks in [12]. In [14], too, no power system integration of the charging processes of electric trucks is considered. Ref. [18] investigates the influence of truck charging demand at depots on real substations in Texas. The effects of controlled and uncontrolled truck charging at depots on energy costs are examined in [19] using the example of the tariffs of three different utilities. The microgrid modeling considered in [21] focuses more on the economic aspects of the energy system, including the day-ahead market. Grid topology and its utilization are integrated in the form of constraints in the economic analyses. Ref. [22] analyzes the required grid connection capacity at three prototype truck charging sites and their development depending on the charging station density, vehicle volume, and the year considered. Ref. [24] investigates the effects of charging demand at fast-charging locations for trucks using four different grid models. Three positions of charging stations in the grids (best, good, and worst) are varied to compare the performance of different voltage control methods [24]. Ref. [25] derives exemplary fleet charging profiles and simultaneity factors from modeling the driving behavior of commercial electric vehicle fleets, but these only apply to light electric vehicles such as passenger cars and light commercial vehicles. Ref. [26] quantifies flexibility potentials, but does not investigate grid impacts of fleets. Ref. [28] deals with the impact of electrified light-, medium-, and heavy-duty electric vehicles on a coordinated distribution and transmission system combined with different load and renewable generation data. This causes system overloads in the exemplary grid model considered in Texas [28].

In summary, an analysis of the state of the research on grid integration of battery electric trucks shows that transferable approaches to charging demand modeling are often lacking, focusing instead on individual use cases. However, these approaches should be individually appliable to different fleets, vehicle types, and charging locations. At the same time, many studies determine the charging demand of vehicles, but only occasionally address how this charging demand affects the power grid and almost never address how the results can be specifically integrated into grid planning. In this paper, a methodology is presented by which the charging demand of different truck weight classes can be modified at characteristic truck charging locations. The method is based on an extension and abstraction of the truck charging demand modeling methodology from [30,32] and can be transferred from there to any individual charging locations. By applying the method to exemplary depots, initial characteristic values for use in power system planning are derived. The truck charging demand modeling approach is presented below.

3. Location-Based Truck Charging Demand Modeling at Logistics Centers

Logistics centers will be one of the main charging locations for battery electric trucks in the future. It is therefore essential to be able to quantify the charging demand of trucks at these centers. This chapter presents the approach developed in this paper for modeling the charging demand of trucks at logistics centers. The methodology is based on a further development of [30,32]. For this purpose, the charging demand modeling approach from [32] was transferred to the use case of logistics centers. Extensive data on the categorization of logistics center types were taken into account. In contrast to [30], the methodology does not allow for the simulation of one single logistics center based on its individual data, but rather the simulation of any logistics center depending solely on its size and type. The methodology in this paper was implemented in Python.

3.1. Modeling Objective

The aim of the charging demand modeling is the time series-based quantification of the total local charging demand $P_{L_1}\left(t\right)$ of all $n$ arriving trucks $V$ at a single logistics center $L_1$:

$$P_{L_1}\left(t\right)=\sum _{j=1}^n{P}_{V_j,L_1}\left(t\right).$$

(1)

This total local charging demand is determined by the sum of the charging demand of all single trucks $P_{V_j,L_1}\left(t\right)$ at the logistics center. Figure 1 illustrates the composition of the results schematically. The following chapters explain how these individual and total charging profiles can be determined.

3.2. Modeling Flow

The charging profile modeling of electric trucks at logistics centers can be divided into four steps:

• Logistics center modeling;
• Electric truck fleet generation;
• Charging demand quantification;
• Charging profile generation.

Figure 2 schematically illustrates the process of modeling the truck charging demand at logistics centers, including the required input data and the generated output data. The individual modeling steps are shown in blue in Figure 2, the required input data in orange, and the generated output data symbolizing intermediate results in gray. The results of the charging profile generation are the individual and total charging profiles $P_{V_j,L_1}\left(t\right)$ and $P_{L_1}\left(t\right)$ described.

For logistics center modeling, customization parameters and site characteristics are required as input data to model the number of trucks arriving at the center under consideration, as well as their arrival and idle times and size classes (step 1). In step 2, the arriving electric truck fleet at the logistics center is generated. Based on mobility data and electric truck parameters, each arriving truck from step 1 is assigned a battery capacity, range, and driven trips. Depending on a chosen charging scenario, the energy demand, charging duration, and minimum necessary charging power can be quantified for each truck within the charging demand quantification (step 3). This allows the generation of the charging profiles for each truck at the logistics center as well as the determination of the total local charging demand (step 4). In the following chapters, the methodology behind the four modeling steps is presented in more detail.

3.3. Logistics Center Modeling

As part of the logistics center modeling, the logistics center under consideration is first specified by customization parameters before thedaily arriving trucks are modeled.. Their arrival and idle times and their types are determined on this basis. The parameters and their values considered in this paper are summarized in

Table 1. Customization parameter overview.

Customization Parameter	Value
Simulation period	(start date, end date)
Simulation region	EU region
Site type	({distribution center, general cargo depot, freight forwarding center, warehouse, parcel depot})
Site size	building area

.

A distinction is made between four different customization parameters. These are simulation period, simulation region, site type and site size. Simulation period and region are used to correctly model the successive days. Site type and size in turn allow a realistic replica of the location. Here, a distinction is made between five logistics center types. According to [33], the number of arriving trucks at a logistics center can be derived from the site size. This can be taken into account via the building area of the logistics centers in the modeling.

From the specification of the logistics center under consideration, the arrival behavior of trucks can be modeled using standardized site characteristics of the different logistics center types.

Table 2. Overview of logistics center types inclusive of typical size, number of daily arriving trucks, and distribution of truck weight classes (data based on [33] combined with own assumptions).

Site Type	Building Area/ha	Number of Daily Trucks 1/-	Truck Weight Classes 3/%
			3.5 t	7.5 t	18 t	>18 t
distribution center	1.25 ha	162	3	3	47	47
general cargo depot	0.75 ha	537	0	0	50	50
freight forwarding center	1 ha	166	0	0	50	50
warehouse	0.8 ha	73	3.75	3.75	46.25	46.25
parcel depot 2	0.75 ha	537	30	30	20	20

¹ Sum of trucks arriving within one working day per hectare building area. ² In this paper, the parcel depot is assumed to be a separate type of logistics center; in [33] it is a special form of general cargo depot. ³ In [33], a distinction is made between trucks up to and over 7.5 t. In this paper, the vehicle shares of these two classes are evenly distributed between two classes up to and two classes over 7.5 t.

and Figure 3 show the site characteristics for the five different logistics center types considered in this paper: distribution center, general cargo depot, freight forwarding center, warehouse, and parcel depot. The different types of logistics centers are based on [33], based on their type of use in the logistics process. While Table 2 shows the relationship between building area and the number of trucks arriving daily per center type as well as the distribution of different truck weight classes, Figure 3 shows the arrival and departure behavior of the trucks. Due to their usage characteristics, the logistics center types differ not only in terms of building area and the truck weight classes arriving but also in terms of the time of arrival and departure of the trucks.

The number of trucks arriving at general cargo depots and parcel depots is particularly high. The arriving fleets in turn differ in their weight class. Significantly more light trucks arrive at parcel depots than at the other logistics center types. The timing of arrivals and departures is also very different. At distribution centers and warehouses, arrivals and departures are only recorded during the day during opening hours. The other three logistics center types, on the other hand, operate 24 h a day. There are also differences in terms of whether a particularly large number of vehicles arrive at the same peak times, as is the case with general cargo depots, or whether they are more evenly distributed. In addition, the idle times at the centers are different. At the parcel depot, vehicles are parked overnight, and at the warehouse, they leave immediately after loading or unloading goods.

For each day of the simulation period from Table 1, the number of trucks arriving daily and their weight classes can be determined from Table 2, depending on the type of logistics center and its specified building area. Using the arrival and departure distributions from Figure 3, the arrival and departure times and the resulting idle time can be determined for each truck.

3.4. Electric Truck Fleet Generation

The results of the first modeling step are the type, arrival time, and idle time for each truck arriving at the logistics center. The next step is to electrify the incoming fleet at the logistics center as part of the electric truck fleet generation. Therefore, each truck is assigned a battery capacity and range of an electric truck model of the same weight class based on electric truck parameters. In order to map the variability between different models, this paper uses data on battery capacity and range from 60 real electric trucks of different weight classes based on a market analysis from [30]. Figure 4 shows an overview of the results of the market analysis for the battery capacity and range of the truck models, differentiated according to their weight class. As the weight classes increase, so do the battery capacities of the trucks, but also the range of fluctuation in the manufacturers’ specifications. The ranges also vary depending on the weight class. A correlation between heavier trucks and higher ranges can only be seen for trucks over 3.5 t in Figure 4. With the current state of battery technology, trucks of 3.5 t are often equipped with a higher battery range than is necessary for the majority of their daily mileage (compare with Figure 5).

To determine the charging demand of the trucks at the logistics centers described, the amount of energy to be recharged must be quantified. This depends on the battery capacity of the truck and its consumption and the trip distance traveled before or after arriving at the logistics center. By using mobility data, real journeys can be taken into account in the charging demand calculation. This paper uses mobility data from Motor Vehicle Traffic in Germany surveys [34,35]. In general, any mobility data sets that allow conclusions to be drawn about individual trip lengths can be used. Figure 5 shows an overview of the distribution of the lengths of individual trips and daily mileage for the four truck weight classes under consideration. It can be seen that the routes become longer as the weight class increases. To simulate the mobility behavior of each truck arriving at the logistics center, a trip before and after arrival is randomly drawn from the mobility data set for each truck depending on its weight class.

3.5. Charging Demand Quantification

To determine the charging demand of each truck at the logistics center in the third step of the modeling, information on the charging scenario under consideration is required in addition to the results from the previous steps. The composition of a charging scenario as a vector $\mathit{B}$ consisting of six charging scenario parameters is shown in Equation (2). The meaning of the parameters and their possible values are listed in

Table 3. Charging scenario parameters.

Charging Scenario Parameter	Value
$\mathrm{Available}\mathrm{charging}\mathrm{power}\mathrm{per}\mathrm{truck}{P}_{\mathrm{v}\mathrm{e}\mathrm{r}}$	({technically possible value in kW})
$\mathrm{Charging}\mathrm{point}\mathrm{availability}{p}_{\mathrm{L}\mathrm{I}\mathrm{S}}$	$(\text{{}{0<p}_{\mathrm{L}\mathrm{I}\mathrm{S}}\le 1$})
$\mathrm{Target}\mathrm{SOC}\mathrm{at}\mathrm{arrival}{SOC}_{t_{\mathrm{A}},soll}$	$(\text{{}0\le {SOC}_{t_{\mathrm{A}}}<1$, last trip-dependent})
$\mathrm{Target}\mathrm{SOC}\mathrm{at}\mathrm{departure}{SOC}_{t_{\mathrm{D}},soll}$	$(\text{{}0<{SOC}_{t_{\mathrm{D}}}\le 1$, next trip-dependent})
$\mathrm{Additional}\mathrm{charging}\mathrm{demand}\mathrm{coverage}b$	({limited, unlimited})
$\mathrm{Charging}\mathrm{mode}l$	({immediate, delayed, uniform, flexible})

.

$$\mathit{B}=\left(\begin{array}{cccccc}{P}_{\mathrm{v}\mathrm{e}\mathrm{r}}& p_{\mathrm{L}\mathrm{I}\mathrm{S}}& {SOC}_{t_{\mathrm{A}},soll}& {SOC}_{t_{\mathrm{D}},soll}& b& l\end{array}\right)$$

(2)

The course of the charging curve of a truck is significantly determined by the available charging power per truck $P_{\mathrm{v}\mathrm{e}\mathrm{r}}$. It is assumed that each truck can charge with the available charging power. This is not the case in reality, but it does allow us to look to the future, where charging powers of up to 3750 kW have been announced for trucks in accordance with the Megawatt Charging System (MCS) [36]. This modeling also assumes charging with constant power up to the target ${SOC}_{t_{\mathrm{D}}}$ instead of other charging curves, e.g., the constant current constant voltage (CCCV) method. This is due to the fact that delays in the charging process are intolerable from a logistics perspective in the truck segment. For this reason, many manufacturers design truck batteries to be larger than specified to the user in order to be able to guarantee high charging power until the battery is fully charged. The availability of charging infrastructure for each incoming truck is also modeled using the parameter $p_{\mathrm{L}\mathrm{I}\mathrm{S}}$. This indicates whether several trucks have to share the available charging power.

By specifying the state of charge on arrival and departure ${SOC}_{t_{\mathrm{A}}}$ and ${SOC}_{t_{\mathrm{D}}}$ of a truck at the logistics center, variation in the charging demand is mapped. The arrival SOC ${SOC}_{t_{\mathrm{A}}}$ can either be dependent on the previously driven route, which means that only this demand needs to be recharged, or can be specified by fixed values. The same applies to the departure SOC ${SOC}_{t_{\mathrm{D}}}$. It allows the effects of recharging fixed battery capacities to be compared with the recharging of single or daily routes driven. The energy requirement of each truck can be determined from the ${SOC}_{t_{\mathrm{A}}}$ on arrival and the ${SOC}_{t_{\mathrm{D}}}$ on departure combined with its battery capacity. Using the available charging power $P_{\mathrm{v}\mathrm{e}\mathrm{r}}$, this allows the necessary charging duration to be determined. In addition, the minimum necessary charging power $P_{\mathrm{m}\mathrm{i}\mathrm{n}}$ can be determined from the quotient of energy demand and idle time.

3.6. Charging Profile Generation

In the last step of the modeling, the single charging profiles of each truck at the logistics center are modeled and aggregated to the total charging profile of the logistics center. The results from the previous steps are used in combination with the charging scenario parameters.

First, it is determined what to do if the idle time is exceeded by the charging time. The charging scenario parameter for covering the additional charging demand $b$ from Table 3 specifies whether charging only takes place during the actual original idle time of the truck at the charging location or whether, if the charging demand cannot be covered during this period, the idle time is extended in order to continue charging to ${SOC}_{t_{\mathrm{D}}}$.

Second, the charging mode $l$ indicates whether charging is uncontrolled or controlled. In this work, a distinction is made between immediate charging, maximum delayed charging, uniform charging with minimum required charging power, and flexible charging. Figure 6 schematically shows the differences between the various charging modes. With immediate charging, the charging process starts on arrival at the charging location. Charging takes place at the maximum charging power available for the vehicle $P_{\mathrm{v}\mathrm{e}\mathrm{r}}$. This allows the charging process to be completed as early as possible. With delayed charging, the charging process is postponed so that it ends when the vehicle departs. Accordingly, it starts later. However, this still ensures that the same charging demand can be met as with immediate charging. Charging also takes place with the available charging power $P_{\mathrm{v}\mathrm{e}\mathrm{r}}$. The first two charging modes are contrasted with uniform charging. Here, charging is constant over the entire time the vehicle is present. This means that the charging power no longer corresponds to the available charging power $P_{\mathrm{v}\mathrm{e}\mathrm{r}}$, but to the minimum power required to cover the charging demand during the limited idle time $P_{\mathrm{m}\mathrm{i}\mathrm{n}}$. With flexible charging, the charging process reacts to an external signal and changes the charging power accordingly between 0 and the available charging power. Nevertheless, the vehicle’s entire charging demand is covered.

A special case occurs when the vehicle’s charging demand is greater than the charging capacity available in the given period of presence. As a result, there is no more flexibility potential in the charging process. This means that the curves for immediate, delayed, and flexible charging are the same. In the case of uniform charging, the minimum charging power required is greater than the power actually available.

4. Results

The methodology described for location-based charging profile modeling of electric trucks is used in this paper to analyze the charging demand at five model depots. In doing so, not only the differences between the logistics center types but also the resulting differences between the modeled charging scenarios are addressed. In the following sections, the model parameters in the case study are discussed first, before the results with regard to the charging demand are discussed. Finally, based on the results, initial characteristic values for deriving peak load parameters for logistics centers for use in power system planning are presented.

4.1. Case Study

In this case study, the five different types of logistics centers are considered as charging locations: distribution center, general cargo depot, freight forwarding center, warehouse, and parcel depot. The size of the locations and the number and type of trucks arriving there are presented in Table 2. This means that the sizes of the centers correspond to typical representatives of their types.

Table 4. Case study customization parameter values.

Customization Parameter	Value
Simulation period	(1 January 2023, 31 December 2023)
Simulation region	Germany: Baden-Württemberg
Site type	({distribution center, general cargo depot, freight forwarding center, warehouse, parcel depot})
Site size	building area according to Table 2

shows the values of the customization parameters for the simulations.

Table 5. Case study charging scenario parameters.

Charging Scenario Parameter	Value
$\mathrm{Available}\mathrm{charging}\mathrm{power}\mathrm{per}\mathrm{truck}{P}_{\mathrm{v}\mathrm{e}\mathrm{r}}$	3750 kW
$\mathrm{Charging}\mathrm{point}\mathrm{availability}{p}_{\mathrm{L}\mathrm{I}\mathrm{S}}$	$1$
$\mathrm{Target}\mathrm{SOC}\mathrm{at}\mathrm{arrival}{SOC}_{t_{\mathrm{A}},soll}$	$(\text{{}0$, last trip-dependent})
$\mathrm{Target}\mathrm{SOC}\mathrm{at}\mathrm{departure}{SOC}_{t_{\mathrm{D}},soll}$	$1$
$\mathrm{Additional}\mathrm{charging}\mathrm{demand}\mathrm{coverage}b$	limited
$\mathrm{Charging}\mathrm{mode}l$	({immediate, delayed, uniform, flexible})

shows the values of the charging scenario parameters. As the focus in this work is on the theoretically possible results, the maximum available charging power of 3750 kW is assumed. This allows the realistically required charging power to be investigated without having to assume time restrictions. In addition, the maximum flexibility potential can be estimated, which can decrease with less available charging power. It is assumed that charging infrastructure is available for every truck arriving at the charging location. In addition, the results of fully charging the truck batteries compared to recharging the previously traveled route are compared in terms of charging demand. All four different charging modes—immediate, delayed, uniform, and flexible—are analyzed. This results in a total of eight different charging scenarios: four for the full charging scenario and four for the trip-dependent charging scenario. These four differ only in their charging mode. The methodology described in Section 3 was used to model the weekday charging demand for the five different logistics center types in the various charging scenarios. The results are presented in the following subsections.

4.2. Charging Demand Analysis for Uniform Charging

In order to obtain an initial overview of the charging demand of trucks at the various logistics centers and the charging infrastructure required for this, the first step is to analyze the charging demand for uniform charging. This means that each arriving truck charges with the charging power that can just cover the charging demand by providing it evenly during the entire time the truck is at the logistics center. This corresponds to the charging mode in Figure 6c. Particular attention is paid to the comparison of the resulting charging time series between the logistics centers themselves and between full charging and last trip charging.

4.2.1. Load Profiles

Figure 7 shows the weekday load profile of truck charging demand at the different logistics center types for uniform charging. A distinction is made between the recharging scenarios of full charging and last trip charging.

The very different arrival and departure behavior of the trucks at the centers from Figure 3 is also reflected in the results of the charging demand. While peak loads are to be expected at distribution centers and warehouses during the day, at general cargo depots and parcel depots, these tend to be in the early morning and evening, as the vehicles are not on-site during the day. The freight forwarding center is a hybrid of the other centers. The level of peak loads and the energy demand also differs significantly between the centers. At the general cargo depot, it is significantly higher than at the other centers due to the particularly large number of heavy trucks. At centers where trucks arrive more evenly throughout the day, such as warehouses and distribution centers, the peak loads are correspondingly lower. This shows the relevance of distinguishing between the different types of logistics center. The three-hour structuring of the peak loads is not generally dependent on logistics. This results from the three-hour resolution of the input data (compare to Figure 3), which in combination with uniform charging means that the highest load always occurs at the end of the three-hour interval. The aim here should be to refine the database in future in order to obtain even more realistic results. The comparison between full charging and last trip charging shows that the charging demand for last trip charging is only around a third, both in terms of peak loads and energy demand. Which charging curve will result at the logistics centers in the future depends on whether recharging is possible at every truck stop location or whether the battery is driven as empty as possible instead. However, the two scenarios shown here indicate a range in which the values can vary.

4.2.2. Charging Power Demand

In addition to the temporal behavior of the load profiles, in the area of truck charging, what charging powers are actually required in order to integrate the charging into the existing logistics processes without delays is particularly interesting. The term megawatt charging is often used here without quantifying how often it is actually required. Figure 8 shows the probability of the minimum charging power required per truck to cover the charging demand within its regular idle time. A distinction is made between full charging at the top and last trip charging at the bottom as well as the different logistics center types. The fact that the idle times and the type of trucks arriving at the centers are different means that the charging power required also differs. It is generally noticeable that regardless of the scenario and logistics center type, megawatt charging is only necessary for a small proportion of the charging processes. This is most likely to be the case at the warehouse location type, as the vehicles are parked for much shorter periods here than at the other centers. In many cases, however, slow charging with less than or equal to 43 kW is also sufficient. At the parcel depot in particular, this is sufficient to fully cover the charging requirements in 60% to 85% of cases. If the battery needs to be fully charged, the charging power is correspondingly higher than with last trip charging.

4.3. Charging Flexibility Potential Analysis

Depending on the charging behavior, the load profiles at the logistics centers can vary. At the same time, available charging powers that are higher than the minimum charging power required in the previous section offer the possibility of making charging demand more flexible. In this section, the effects of immediate and delayed charging modes are first examined in comparison to uniform charging, and then flexible charging is discussed.

4.3.1. Effects of Different Charging Modes

Although uniform charging during a truck’s stay, as discussed in the previous section, is helpful for estimating the minimum charging power required, in reality, it does not occur as standard. This is due to the fact that for uniform charging, a charging connection must be provided for each vehicle for the entire duration of its stay. At the same time, the vehicle’s charging demand must be known from the outset in order to adjust the charging power accordingly. In order to further restrict the value range of the load profile from reality, immediate and delayed charging are examined here. With immediate charging, the vehicle starts directly on arrival with the maximum available charging power and recharges based on demand as quickly as possible. With delayed charging, on the other hand, the charging process is started as late as possible so that the charging process finishes exactly on departure. Figure 9 shows the results of these two charging modes in comparison to the uniform charging previously considered. Only the full charging scenario is shown. As a maximum scenario, it was assumed that each vehicle can recharge with the maximum of the megawatt charging standard of 3750 kW. This means that hardly any charging process prolongs the downtime at the logistics center. The effects of the different charging modes on the load profiles vary. At centers with many distributed charging processes during the day, such as the distribution center, warehouse, and freight forwarding center, immediate charging results in less simultaneity in the charging processes, and thus lower peak loads than with uniform charging occur. At the general cargo depot and the parcel depot, a large number of trucks arrive and depart at the same time, which means that both immediate charging and delayed charging cause high peak loads due to high simultaneities. In general, it can be seen that the charging mode can have a strong impact on the load profile. However, this also creates new flexibility potentials at the logistics centers that can be used. At best, the charging load profile is adapted to the conventional load profile of a logistics center and to any local generation. The next subsection will therefore take a closer look at the time-shift potential of the load profiles.

4.3.2. Temporal Shifting Potential

The results of the previous sections have shown that charging electric trucks at logistics centers can cause new peak loads at these locations. The extent to which these new loads can be flexibly adapted is of interest with regard to the appropriate dimensioning of the grid connections, but also taking into account the increasing flexibility potential in the electricity grids. By knowing the idle time of the trucks at the logistics centers as well as the necessary charging time at fixed charging powers, the charging demand modeling approach allows an analysis of the temporal shift potential of the charging loads. Figure 10 shows the time-shift potential of the cumulative charging loads for immediate full charging. The portions of the weekday load profiles that can be shifted by a certain period of time are colored. The consideration of individual charging powers of 3750 kW allows an outlook on the maximum available flexibility potential. At lower charging powers, as shown in Figure 11, the flexibly shiftable proportions of the charging loads decrease accordingly. High flexibility potentials can be seen at the general cargo depot and the parcel depot in particular. This is due to the idle times of the trucks arriving there overnight. Half of the peak load between 3 p.m. and 6 p.m. can be shifted by more than 12 h. Only a very small proportion of the load between 3 p.m. and 9 p.m. cannot be shifted.

4.4. Initial Characteristic Values for Power System Planning

Even if the location-based charging demand modeling approach for electric trucks at different logistics depots can be adapted to the characteristics of individual depots, its detailed modeling is not always suitable in practice. For power system planning by grid, it is often sufficient to assume peak loads, possibly with knowledge of their probability of occurrence. In this paper, therefore, easily applicable peak loads were derived from the weekday load profiles. Here, full charging and last trip uniform charging are considered. Figure 12 shows an overview of the mean weekday peak loads occurring per logistics center type and building area. Depending on the type of logistics center under consideration and its building area, the appropriate peak load value can be read from the graphs.

5. Conclusions

In this work, a method for modeling the charging demand of electric trucks at logistics centers was presented. Compared to the existing state of research, it allows the quantification of the time-dependent charging demand of electric trucks at different types of logistics centers as well as the transfer of the methodology to the characteristics of individual charging locations. The derivation of characteristic values for peak load depending on the size and type of logistics center allows the results to be easily transferred into practice.

The methodology for modeling the charging demand is based on the combination of data on the arrival and departure behavior of trucks at logistics centers and their mobility behavior with data on consumption and range of battery electric truck models. When modeling the logistics centers, a distinction was made between five different types. These differ not only in terms of their logistical processes and thus timing but also in the type and number of trucks arriving. The methodology was used to quantify the charging demand of electric trucks at one model site for each type of logistics center. The charging of electric trucks at these locations can result in peak loads in the one- to two-digit megawatt range at the locations, but vary greatly depending on the type of logistics center. The temporal behavior of the charging load also differs depending on the logistics processes. At centers like parcel depots, peak loads are to be expected in the morning and evening, while the charging demand at centers like warehouses is more evenly distributed throughout the day. The results not only indicate the relevance of the separate consideration of the logistics center types but also the importance of differentiating between different recharging scenarios. They also make it possible to determine the actual charging powers required per truck at the logistics centers. These are partly in contrast to the currently much-demanded Megawatt Charging System. It can be seen that truck charging at logistics centers can create a new high-power requirement, but also has considerable flexibility potential.

The presented methodology and results of this work serve as the basis for further studies by the authors. These will take a closer look on the comparison of the abstracted results with charging demand data of real logistics centers, the application of the presented methodology to real power system case study analyses, and the development of further characteristic values for power system planning with electric trucks. The limitations of the methodology lie primarily in the database. The time resolution of the logistics center data needs to be increased in order to quantify the resulting peak loads more realistically. The vehicle parameters used also still vary greatly depending on the manufacturer’s specifications. Sensitivity analyses can specify the effects of these varying specifications more precisely. At the same time, the energy consumption of the vehicles should be validated by real consumption measurements.

As much of the research in the area of grid integration of electromobility has so far focused mainly on battery electric cars, there is still a great need for research in the field of grid integration of battery electric trucks. In this way, the number and types of truck charging locations considered can be extended. For this purpose, truck charging demand modeling can be transferred to other typical truck stop locations away from logistics centers, such as charging hubs on highways. Moreover, a comparison of the location-based charging demand modeling methodology with vehicle- or GPS-based models allows the charging demand to be estimated in an even more targeted manner, especially in larger observation areas. The reliably plannable logistical processes and the large truck batteries open up new, previously unused flexibility potentials in the electricity grid. Their analysis can be significantly expanded with regard to bidirectional charging and the specific use of flexibility.